I have an early 2015 MacBook Air, backed up through time machine. If I get a new M2 air, will the time machine transfer all my Microsoft Office programs or will I have to replace them?

3rd party apps can be problematic especially if they're licensed; best to uninstall stand alone Office on old Mac and reinstall on new Mac. The problem is activation. MS thinks you have a new computer, which you do, and that requires re-activation.

In theory, if you have Microsoft 365 the process should be seamless, However; enough post have made it here to show that's not completely the case